Viscous Primitive Equations Research Articles

An Extended Lagrangian Theory of Semi-Geostrophic Frontogenesis

Abstract The Lagrangian conservation law form of the semi-geostrophic equations used by Hoskins and others is studied further in two and three dimensions. A solution of the inviscid equations containing discontinuities corresponding to atmospheric fronts is shown to exist for all time under fairly general conditions, and to be unique if the potential vorticity is required to be nonnegative. Computational results show that this solution agrees with high resolution solutions of the viscous semi-geostrophic equations. The solution, however, disagrees with that obtained from the two-dimensional viscous primitive equations. An important aspect of the difference is that the semi-geostrophic solutions allow the front to propagate into the interior of the fluid while the primitive equation solutions do not. This is discussed. If correct, it may indicate a tendency for a separation effect in the atmosphere where frictional effects are present.

Statistical dynamics of internal gravity waves-turbulence

Abstract Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, Pz , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure. The sta...